At the same age, metallicity, and alpha-enhancement, sodium is a more effective tracer of the young and old sequences of the Milky Way disc

The third data release (DR3) of the GALactic Archaeology with High Efficiency and Resolution Multi-Element Spectrograph (HERMES; at the Anglo-Australian Telescope, Sheinis et al., 2015), hereafter GALAH, is a high-resolution (R $\sim$28000) spectroscopic sample of stars in the Milky Way Galaxy containing atmospheric parameters and abundance information for nearly 600 000 stars as of the current data release (Buder et al., 2021).

GALAH is an extensive stellar spectroscopic survey like SEGUE (Yanny et al., 2009), RAVE (Kordopatis et al., 2013), and APOGEE (Anders et al., 2014). These surveys serve as a window to study the formation and evolutionary history of the Galaxy and astrophysical processes using traces of gas that have been transported and incorporated into the formation of generations of stars throughout the Galactic history. Primarily, GALAH targets relatively bright stars in the magnitude range of $9<V<14$, which are typically closer than $2\,\mathrm{kpc}$. In GALAH DR3, up to 30 elemental abundances are provided for each star, along with their uncertainties and quality flags. Additional physical properties such as surface gravity, effective temperature and age are also reported. The ages were determined using the Bayesian stellar parameter estimation code (BSTEP; Sharma et al. 2018).

GALAH DR3 provides analyses of stellar spectra from the HERMES spectrograph, which covers four wavelength bands in the optical and near-infrared (4 713 – 4 903, 5 648 – 5 873, 6 478 – 6 737, and 7 585 – 7 887 Å, Sheinis et al., 2015). The abundances were derived using the 1D MARCS model atmospheres (Gustafsson et al., 2008), and a modified version of the Spectroscopy Made Easy (SME) spectrum synthesis code (Valenti & Piskunov 1996; Piskunov & Valenti 2017). Of these elements, 11 were computed using TE (Amarsi et al. 2020) and the remaining 19 elements were determined using local thermodynamic equilibrium (LTE). Na is among the $11$ elements for which NLTE effects were included in the analysis of GALAH spectra. The abundance analysis is preceded by a step that derives the global stellar parameters from the spectra, namely effective temperature ($T_{\text{eff}}$), surface gravity ($\log g$), iron abundance [Fe/H], micro-turbulence velocity ($v_{\text{mic}}$), broadening velocity ($v_{\text{broad}}$) and radial velocity ($v_{\text{rad}}$). The elemental abundances of element ‘A’ to element ‘B’ are expressed as logarithmic ratios of number densities $N$, that is,

where abundances are normalised to the solar values and are defined in the usual way as [X/Fe] $=$ [X/H] $-$ [Fe/H].

The ages of stars in GALAH DR3 were computed using a Bayesian Scheme known as the Bayesian Stellar Parameters estimator (BSTEP Sharma et al., 2018) with an elaborate step-by-step distribution given in section $3$ of Sharma et al. (2018).

To assess the nature of the abundance enrichment and its correlation with stellar age, we apply an overall quality cut and then divide thea into a smaller sample of solar-type stars, which are defined as cool main-sequence dwarfs located below the red edge of the classical instability strip (including spectral types from late F, G and up to K dwarfs, Soderblom & King, 1998; García & Ballot, 2019) for the GALAH data, this can be applied through the following masks:

We employ basic quality cuts to select only unflagged measurements (Eq. 2). Because our study relies on reasonably determined ages, we further limit our sample to stars with either less than $20\%$ age uncertainty or age uncertainties below $2\,\mathrm{Gyr}$ (Eq. 3). To ensure a reasonable quality of measurements, we set a lower spectrum quality cut of signal-to-noise in the green CCD of 50 per pixel (Eq. 4). We further limit our sample to solar-type stars via Eqs. 5 and 6 following the definition of Nissen et al. (2020).

Whenever we use elemental abundances [X/Fe], we further apply a quality cut of

where X replaces the respective element, e.g. Na, for acceptable sodium measurements.

In Fig. 1b) we show the [Na/Fe] versus [Fe/H] relation with bin median ages in a step size of $2$ Gyr. The important takeaway is that within all age bins explored in Fig. 1b, stars are visibly more enriched in [Na/Fe] at high metallicity for ages between 4 – 6 Gyr. The resulting differences in [Na/Fe] enhancement for different ages motivated us to test its potential to separate stars of the young and old sequence of the Milky Way disc.

The Milky Way’s stellar disc is a complex structure, and its formation and evolution are still widely debated (e.g. Katz et al., 2021). Several surveys have provided large statistical samples of stars with detailed chemical abundances, such as RAVE (Kunder et al., 2017), Gaia-ESO (Randich et al., 2013), APOGEE (Alam et al., 2015), LAMOST (Zhao et al., 2012), and GALAH (Buder et al., 2018), combined with very precise Gaia astrometry (Lindegren et al., 2018), making it possible to examine the formation of the Galactic disc with an unprecedented level of detail. The sample includes mainly thin and thick disc stars of all ages selected based on various criteria, such as the relative abundance of alpha-elements and stellar ages within the old sequence of the Milky Way disc. Due to the overlap of the thin and thick disc stars, several studies (see for instance Lee et al., 2011; Delgado Mena et al., 2021; Bensby et al., 2014; Recio-Blanco et al., 2014; Hayden et al., 2017) have devised preliminary techniques to separate the contamination of the two-disc sequences. However, kinematics and chemo-dynamics have proven to be rather inaccurate in distinguishing both sequences, especially at intermediate ages (Hayden et al., 2017) in the metallicity range of $-0.3$ to $+0.5$ dex, where both sequences overlap (e.g. Bensby et al., 2014).

The Milky Way’s stellar disc is a complex structure, and its formation and evolution are still widely debated (e.g. Katz et al., 2021). Several surveys have provided large statistical samples of stars with detailed chemical abundances, such as RAVE (Kunder et al., 2017), Gaia-ESO (Randich et al., 2013), APOGEE (Alam et al., 2015), LAMOST (Zhao et al., 2012) and GALAH (Buder et al., 2018), combined with very precise Gaia astrometry (Lindegren et al., 2018), making it possible to examine the formation of the Galactic disc with an unprecedented level of detail. The sample includes mainly thin and thick disc stars of all ages selected based on various criteria, such as the relative abundance of alpha-elements and stellar ages within the old sequence of the Milky Way disc. Due to the overlap of the thin and thick disc stars, several studies (see for instance Lee et al., 2011; Delgado Mena et al., 2021; Bensby et al., 2014; Recio-Blanco et al., 2014; Hayden et al., 2017) have devised preliminary techniques to separate the contamination of the two-disc sequences. However, kinematics and chemo-dynamics have proven to be rather inaccurate in distinguishing both sequences, especially at intermediate ages (Hayden et al., 2017) in the metallicity range of $-0.3$ to $+0.5$ dex, where both sequences overlap (e.g. Bensby et al., 2014).

We continue our analysis by reproducing the selection of young and old sequences in the age-abundance plane similar to Nissen et al. (2020). However, contrary to Nissen et al. (2020), who use a selection in the age vs. [Fe/H] space, we select stars via age and [Na/Fe]. Thick and thin solar-type stars from the study of Nissen et al. (2020) are superimposed over the GALAH DR3 solar-type stars data (see Fig. 1).

Fig 1a, in particular, shows an initial selection (hereafter standard cut) based on a separation ‘by eye’ of the Nissen et al. (2020) stars as an orange line. We classify stars as young or old whether they are below or above the line as:

where $\tau$ represents the stellar age. We discuss the sensitivity of our results to variations of our standard cut in Sec. 3.3 in which we test the robustness of our selection criteria for the GALAH data sample. For the smaller data set ofNissen et al. (2020), this cut is robust mainly due to the difference of [Na/Fe] rise of $\sim~{}0.30$ dex around $5\,\mathrm{Gyr}$.

Our selection now allows us to assess the age-abundance distribution for all other elements in Fig. 2, which shows the solar-type thick (red colour) and thin (royal blue colour) disc stars from Nissen et al. (2020) overlaid on GALAH DR3 solar-type thick (orange) and thin disc (sky blue) stars respectively. Further to this, we show the distribution of our stellar sample population with contours in the [Fe/H]–age plane in Fig. 3. The GALAH DR3 solar-type population in our work follows a similar trend in separation in the [Fe/H] vs. age space as depicted in Nissen et al. (2020). Since our dataset comprises nearly 2 orders of magnitude more stars than the Nissen et al. (2020) sample, it includes stars at about $6.3$ Gyr, the age that roughly corresponds to the transition between young and old sequence and is sparsely populated in the Nissen et al. (2020) work (see Section 4.5 for further discussion). We note that the ages of younger stars tend to be larger than those of Nissen et al. (2020), but the trends agree in a relative sense, which thus does not change the implications of this study. Recent works e.g. Xiang & Rix (2022) and Anders et al. (2023) have confirmed the existence of two sequences in the [Fe/H]–age diagram.

While we have established the clear upturn of [Na/Fe] for the old sequence, the trends for other elements are more diverse. While other odd-Z elements like aluminium (Al) and scandium (Sc) also demonstrate a rise in their abundance with decreasing stellar age, their rise is less pronounced than that of sodium (Fig. LABEL:fig:scatter). When we consider potassium (K), another odd-Z element, it shows a unique trend (i.e., it remains flat), though we note K is less well-constrained in the [X/Fe] axis. Furthermore, some alpha elements (i.e., C, O, and Ca) show overall decreasing trends as we consider younger stellar ages; see also Tab. 1. On the other hand, elements near the iron peak (i.e., Cr, Mn, Ni, Cu, Co and Zn) demonstrate increasing upward trends. More so, the neutron capture element yttrium (Y) remains flat, while barium (Ba) shows a decreasing trend. Section 4.2 discusses possible underlying reasons for these trends.

Here we test how robust our age-abundance trends are regarding the particular selection function (cut guided by eye) chosen in the [Na/Fe]-age plane. The results of the age-abundance trends for each element are displayed in Fig. 4. The outcomes of the linear fits performed on our population of stars are presented in Table 1.

To test the robustness of our [Na/Fe] versus age trend against the details of the choice of the standard cut in Eq. 8, we consider further cuts (as shown in Fig. 6) defined by the equations below:

where $\mathrm{\tau}$ is the age of stars in Gyr. The effect of these various cuts is shown in Fig. 7.

It has been noted that cobalt (Co) has large uncertainty values because only a few lines are present in GALAH DR3. However, for other elements, the trends obtained from different separation cuts agree with the scatter, meaning that the slopes characterising abundance relative to iron with decreasing stellar age all cluster around the same gradient value for the elements investigated. This suggests that the slope estimates for different cuts of each component are in close agreement, indicating a robust selection technique for separating the old sequence from the young sequence.

Sodium is an odd-Z element synthesised in exploding massive stars and dying low-mass stars. In massive stars, Na is synthesised during the hydrostatic carbon burning phase (Cameron, 1959; Salpeter, 1952; Woosley & Weaver, 1995). Also, during the neon-sodium (Ne-Na) and magnesium-aluminium (Mg-Al) cycles in dying low-mass stars, Na is produced (Denisenkov & Denisenkova, 1990) and mixed to the surface (e.g. El Eid & Champagne 1995; Mowlavi 1999; Karakas 2010; Cinquegrana & Karakas 2022).

Owing to the diverse sources from which Na is synthesised, its abundance pattern as a function of metallicity is considered a complex one (Bedell et al., 2018). For instance, the trend of [Na/Fe] first increases with [Fe/H] because of the contributions from massive stars that produce Na and Fe (Bensby et al., 2017, see fig 21); however when the nucleosynthetic products of SNe Ia begin to have a significant impact on a stellar population ${\sim}0.4-1$ Gyr after star formation (Ruiter et al., 2011, see fig. 2), [Na/Fe] starts to drop with [Fe/H]. As a result, the trend of [Na/Fe] over time (i.e., metallicity and age) has been described as a “zigzag” one (McWilliam, 2016). This trend is important for our consideration because the bulge shares the same abundance trend with the thin and thick discs (Bensby et al., 2017). The study of Nissen et al. (2020) reported a rise in [Na/Fe] of $0.15$ dex for the same stellar population at the same age range (5 – 8 Gyr). Similarly, we find that a linear fit to the old sequence at intermediate ages of $5-8$ Gyr gives a gradient value of $0.0260\pm 0.0009\,\mathrm{dex/Gyr}$ , i.e, $0.077$ dex for the stated age range for [Na/Fe]. Also, a steeper rise for [Na/Fe] occurs between the ages of $5-6.3$ Gyr with an abundance gradient of $0.0673\pm 0.0031\,\mathrm{dex/Gyr}$ (see red data points in Fig 5) compared with that of $0.0066\pm 0.0021\,\mathrm{dex/Gyr}$ (see Tab. 1).

We indeed see an explicit “knee” behaviour (McWilliam, 2016) for several elements in our study, with a plateau behaviour for stars aged 8-6.3 Gyr followed by a change in slope – going up or down – from ages 6.3 to 5 Gyr. One may assume then that iron enrichment from SNe Ia becomes more critical around the time of the ${\sim}6.3$ Gyr knee. We can see a decline for some elements relative to iron as we observe younger (generally more metal-rich) stars owing to the (generally long) delay times attributed to SNe Ia (Matteucci & Brocato, 1990; Ruiter et al., 2009; Maoz et al., 2012). An upward trend in [X/Fe] with decreasing age would be expected for some elements, particularly around the iron peak (i.e. Mn, which is mainly synthesized in SNe Ia arising from massive white dwarf stars close to the Chandrasekhar mass limit, Seitenzahl et al., 2013b). However, Na also shows an upward trend with decreasing age, though Na is not canonically associated with SNe Ia but more often with short-lived, massive stars. This means something is driving Na-enrichment other than simply the products of massive stars. The knee effect we see in Na here would be consistent with Na being synthesised by core-collapse supernova progenitors with a metallicity-dependent yield – the ‘metallicity effect’ – which we describe in the following three paragraphs.

Many of the light odd-Z elements only have one stable isotope (e.g., ${}^{23}\text{Na}$ (11p,12n), ${}^{27}\text{Al}$ (13p,14n), ${}^{31}\text{P}$ (15p,16n), ${}^{45}\text{Sc}$ (21p,24n), etc.). These odd-Z stable isotopes are neutron-rich with nuclei having more neutrons than protons. At low progenitor metallicity, a pre-supernova star will have $Y_{e}$ very close to 0.5 in the relevant layers where explosive nucleosynthesis occurs since core helium burning produces mostly self-conjugate nuclei like ${}^{12}\text{C}$,${}^{16}\text{O}$, and ${}^{20}\text{Ne}$. However, with increasing metallicity, more C, N, and O nuclei are already present during hydrogen burning. The CNO cycle turns most of the nuclei present as CNO to ${}^{14}\text{N}$.

Importantly, a main reaction during core helium burning then is ${}^{14}\text{N}(\alpha,\gamma)^{18}\text{F}(\beta^{+}\nu_{e})^{18}\text{O}(\alpha,\gamma)^{22}\text{Ne}$. In effect, by number, most CNO nuclei initially present are turned into ${}^{22}\text{Ne}$, which, owing to the beta-decay of ${}^{18}\text{F}$ is neutron-rich with two extra neutrons. Since the relative number of protons to neutrons is largely conserved for many environments where explosive nucleosynthesis occurs, the extra neutrons available allow the more efficient nucleosynthesis of the neutron-rich odd-Z isotopes.

In contrast, alpha elements (i.e., the even-Z elements such as Mg, S, or Ca) have more stable isotopes that extend from self-conjugate stable nuclei on the alpha-chain [e.g., ${}^{24}\text{Mg}$ (12,12), ${}^{32}\text{S}$ (16,16), ${}^{40}\text{Ca}$ (20,20)] to several neutron-rich stable isotopes (e.g. ${}^{25}\text{Mg}$, ${}^{26}\text{Mg}$, $\ldots,^{48}\text{Ca}$). This means we can make stable even-Z element isotopes at high and low (no) neutron excess. Still, we can synthesise odd-Z elements more efficiently in environments with extra neutrons (which means higher metallicity). Higher progenitor metallicity here also means that the neutron-rich isotopes like ${}^{25}\text{Mg}$ of these even-Z elements are produced in greater abundance; however, this comes at the expense of the also stable ${}^{24}\text{Mg}$ and so the total production of the element Mg is hence overall less affected.

Another potential source of Na-enhancement to reasonably consider is Novae. Novae are (recurring) thermonuclear eruptions on accreting white dwarfs, and could also be considered as a plausible source of Na given their range of delay times (see fig 12, Kemp et al., 2021). However, preliminary work indicates that novae are not a leading contributor to sodium enrichment in the Galaxy above solar metallicity (A. Kemp, Private Comm. 2024).

The increasing trend of [(Na, Al, Sc)/Fe] differs from what we expect based on their canonically assumed primary nucleosynthetic origins. One potential factor leading to an increasing abundance of Na with decreasing stellar age could be the effect of increasing metallicity on Galactic enrichment from core-collapse supernova explosions (Woosley & Weaver, 1994; Kobayashi et al., 2006; Nomoto et al., 2013; Limongi & Chieffi, 2018, see 4.1). Another could be asymptotic giant branch (AGB) stars; AGB stars have been proposed as a possible reason for the rising abundance trend at super-solar metallicity (Shi et al. 2004; Kobayashi et al. 2011; Cinquegrana & Karakas 2022).

For most Fe-group elements, the observed rising trend is consistent with predictions for the existing nucleosynthetic paradigm due to the increasingly dominant role of exploding white dwarfs with time (i.e. as we look at younger stars in the Galaxy, we increasingly see the footprint of SN Ia nucleosynthesis). Furthermore, $\alpha-$elements (i.e., Mg, Si, Ca, and additionally Ti) generally remain flat for the old sequence between ages of $\sim 8-6.3$ Gyr age range, after which there is a gradual decrease (so-called knee; first reported by McWilliam (1997)) in their elemental abundances due to the diminishing contribution of core-collapse SNe and increasing birthrate of SNe Ia. The trend in magnesium (Mg) follows the same age-abundance trend seen in all iron-peak elements in the younger old disc sequence (with a positive gradient), contrary to what we may expect (i.e. that Mg should follow a similar behaviour as other $\alpha$ elements relative to iron and flatten out or become more negative with decreasing age). Also, we find that, light elements (C and O), as well as the neutron capture element Ba show a decreasing trend towards younger stellar ages.

Of the elements that showed enrichment in their abundances, of copper is most prominent, followed by sodium (see Tab. 1). On average, for these elements, more enrichment occurred at around 6.3 Gyr and this manifests as an increase by a factor of $\sim 10$ in their respective gradients. Although copper (atomic number $=29$) and zinc (atomic number $=30$) lie close on the periodic table, they have different age-abundance gradient values. Cu and Zn abundance trends are somewhat flat in the $8$ and $6.3$ Gyr age group. However, Zn quickly rises and remains flat in the $6$ and $5$ Gyr age range. On the other hand, Cu has a gradual but sustained increase in its abundance from ${\sim}6$ Gyr.

While our study focuses on the old sequence of the Milky Way, a similar survey for solar-twin stars belonging to the thin disc was carried out by Spina et al. (2016) to trace the chemical evolution by examining the [X/Fe] versus age for $24$ elements from carbon (C) to europium (Eu). Spina et al. (2016) used the high-resolution and high signal-to-noise UVES optical spectrograph of the VLT to obtain spectra of nine solar twins to make precise estimates of stellar ages and chemical abundances. The study revealed that each class of elements showed a distinct evolution with time, depending on the different characteristics, rates, and timescales of the nucleosynthesis sites from which they are produced. Findings from the study showed that $\alpha$-elements (Ca, Ti, Mg, Si, etc.) are characterised by a [X/Fe] decrease with age, while the iron-peak elements (V, Cr, Mn, Ni, Co, etc.) show an early [X/Fe] increase that peaks at around $6$ Gyr followed by a decrease towards the youngest stars. In addition to previous work by Spina et al. (2016) on Solar twin stars, Buder et al. (2021) compared the Solar twin stars in GALAH DR3 to that of Spina et al. (2016) and found a significant agreement for these elements: O, Na, Si, Ca, Sc, Ti, Mn, Zn, Y, and Ba. However, elements such as Mg and Cr had a slight offset due to few lines being used in the calibration red (see Fig. 15 of Buder et al., 2021). The presence of few lines in our data for Cr is the reason for the offset when compared with other elements that agree with that of Nissen et al. (2020) data.

We appreciate that, at first glance, we have made a seemingly arbitrary cut when fitting the age-abundance trends above and below 6.3 Gyr. However, this decision is also corroborated by previous reports of a knee-age effect by Edvardsson et al. (1993) and McWilliam (1997). Since then, other studies have reported this knee-age effect, mostly seen in $\alpha-$element plots (Bensby et al., 2014; Spina et al., 2016). The occurrence of the knee indicates the onset of the dominant role of (ideally) one nucleosynthesis source relative to another. Various authors have provided different explanations for the presence of the knee phenomenon. One view, proposed by McWilliam (1997), suggests that the knee effect indicates varying star formation rates between distinct stellar populations such as the bulge, halo, and Galactic discs. Another view, expressed by Nissen et al. (2020), suggests that the knee can be interpreted as evidence of gas accretion onto the Galactic disc, with a quenching of star formation in between.

Our work shows the occurrence of the knee-age effect (or elbow-age effect) in most elements considered around 6.3 Gyr. For odd-Z and Fe-peak elements (see Section 4.2), we see an upward trend in the [X/Fe] beyond the knee – which we have coined an elbow – and for light and alpha-elements, we notice a decreasing trend afterwards (classic knee). For elements near the iron peak, we interpret this trend as the point at which SNe Ia start to make a significant impact on chemical enrichment of the stellar population under study, considering that most of these elements are readily synthesised during SN Ia explosions (Thielemann et al., 2002). Furthermore, we also consider the decreasing trend of alpha and light elements as the point where core-collapse supernovae has reached their peak, consequently leading to a decrease in their [X/Fe] as most of these elements are produced through explosions of massive stars (Arnett, 1995; Iwamoto et al., 1999; Kobayashi et al., 2011). We conclude by noting again that the knee-age effect from this work is an indication of the variation in star formation rate due to the differences between older and younger stellar populations. This also suggests that there is a change in how gas is accreted onto the younger stellar sequence, which is influenced by the presence of the older sequence.

One of our motivations was to try and identify a less contaminated selection method of thin and thick disc stars in the high-metallicity regime, where stars significantly overlap in their dynamics and alpha enhancement. To this end, we have reproduced the linear selection in [Fe/H] vs. [Mg/Fe] used by Hayden et al. (2017) in the [Fe/H] vs [Mg/Fe] plane and we show where these stars are in the Age-[Na/Fe] plane in Fig. 8.

To compare how similar our new selection method is to the selection criteria of Hayden et al. (2017), we construct a confusion matrix (see Fig. 9). We see that 59% of the stars are attributed to opposite populations. Most notably, Hayden et al. (2017) would allocate 55% (i.e., 3415 stars) of the old sequence as defined in our work as thin disc stars when using [Mg/Fe] criteria. Also, 4% of young sequence stars (248 stars) as described in this work would be categorised as thick disc stars when using the [Mg/Fe] selection method. In all, only 41% are allocated to the same populations (i.e., 21% thin and 20% thick disc stars).

To further check as to whether our selection method results in less contaminated old and young sequences than the method of Hayden et al. (2017), we also compare the orbital peri-galactocentric distances of the stars from both works. We indeed see a difference in the two populations: we find the older sequence stars are found to have smaller peri-galactocentric distances, e.g. distances closer to the Galactic centre, on average, compared to the younger sequence. We can clearly see a distinction between the old and young sequences, especially between 3–5 kpc from the histogram plot in Fig. 10 (panel a), where both sequences are distinctly differentiated in our Na-based selection compared to the Mg-based selection where they experience more overlap (Fig. 10, panel b). We find a stronger correlation (supporting the notion that old sequence stars are more readily found closer to the inner Galaxy) than Hayden et al. (2017). This significant difference in the allocation of stars to the two populations can have critical implications for the study of abundance trends in the Milky Way – most notably the high-metallicity regime, which is more dominant in the inner Galaxy (Matteucci & Francois, 1989; Recio-Blanco et al., 2014).